Hecke algebras for tame supercuspidal types

2021/01/06 by Kazuma Ohara, Ohara, Kazuma · 1 citation
Mathematics · #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2101.01873

openalex publication_date 2021/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a non-archimedean local field of residue characteristic p≠ 2. Let G be a connected reductive group over F that splits over a tamely ramified extension of F. Yu constructed types which are called tame supercuspidal types and conjectured that Hecke algebras associated with these types are isomorphic to Hecke algebras associated with depth-zero types of some twisted Levi subgroups of G. In this paper, we prove this conjecture. We also prove that the Hecke algebra associated with a regular supercuspidal type is isomorphic to the group algebra of a certain abelian group.

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